中科院数学与系统科学研究院

数学研究所

 

非线性分析研讨班

 

报告人:Prof. Yoshihisa Morita(Ryukoku University, Japan)

题  目:Turing-type instability and stable pattern in a bulk-membrane diffusion model with mass conservation

时  间:2019.10.17(星期四),09 :00-10 :00

地  点:数学院南楼N224室

摘  要:There are a number of mathematical models related to the emergence of cell polarization. In particular, reaction-diffusion systems and bulk-membrane diffusion equations are used for understanding of the mechanism of the polarization. Motivated by those studies for the cell polarization, we deal with coupled bulk-membrane diffusion equations with mass conservation. We establish a Turing-type instability of the equations in the n-dim ball (n=2,3) by investigating the linearized eigenvalue problemand show a stable pattern of the shadow system in a specific case. The main results are due to the work with K. Sakamoto (Hiroshima University).

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报告人:Prof. Tatsuki Kawakami(Ryukoku University, Japan)

题  目:Critical Fujita exponents for semilinear heat equations with quadratically decaying potential

时  间:2019.10.17(星期四),10 :00-11 :00

地  点:数学院南楼N224室

摘  要:In this talk we study the existence/nonexistence of global-in-time positive solutions of the Cauchy problem 
 
where p>1and v  is a radially symmetric function decaying quadratically at the space infinity. We identify the so-called critical Fujita exponent for problem (P) and we show that the critical exponent depends on whether  is subcritical, critical or supercritical. This is a joint work with K. Ishige (University of Tokyo).

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报告人:Prof. Haigang Li(Beijing Normal University)

题  目:Babuska Problem in Composite Materials and its Applications

时  间:2019.10.17(星期四),11 :15-12 :15

地  点:数学院南楼N224室

摘  要:In high-contrast composite materials, the stress concentration is a common phenomenon when inclusions are densely distributed and may possibly touch. It always causes damage initiation and even ultimate failure. This problem was proposed mathematically by Ivo Babuska, concerning the system of linear elasticity, modeled by a class of second order elliptic systems of divergence form with discontinuous coefficients. I will first review some of our results on upper and lower bounds of the grdients by developing an iteration technique with respect to the energy integral to overcome the essential difficulty from the lack of maximal principle for elliptic systems, then present our very recent results on asymptotics of the gradients in dimensions two and three to show the key role of the geometry of the inclusions played in such blow-up analysis.

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